Finite Group Databasebeta

← #14810381

Subgroups — #14810381

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic, complemented
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13076969C211yesmaximal, characteristic
5#13069756C214yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13068922C214yesmaximal
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic
9C11×#1990C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13D11×C4⋊Q8—24no—
14D11×C4⋊Q8—24no—
15C2×#66950C2212yes—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11C2212yes—
18C2×#66941—21no—
19C2×#66941C2212yes—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66880C2214yes—
27#10622706—24no—
28#10622600—21no—
29#10622600—21no—
30#10622598—21no—
31#10622598—21no—
32#10622587C2212yes—
33C2×#66874C2214yes—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622294—24no—
36C11×#340C2214yes—
37#10622188C2212yes—
38#10622167C2214yes—
39C22×Q8×C11—21no—
40C2×Q8×D11—28no—
41C2×Q8×D11—44no—
42C2×Q8×D11—44no—
43C22×C4×D11—22no—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×Dic22—21no—
48C22×Dic22—22no—
49C22×Dic22C2312yes—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59#66997—28no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72#66950—28no—
73C4⋊C4×D11—28no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—24no—
76#66941—28no—
77#66941—24no—
78#66941—24no—
79C42×D11—22no—
80C42×D11—22no—
81#66922—22no—
82#66922—22no—
83#66922—22no—
84#66922D414yes—
85C4×C8×C11—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88(C2×D11)⋊C8—24no—
89#66880—28no—
90#66874—28no—
91C4×C11⋊C8—22no—
92#25902—111nomaximal, Sylow
93C23×D11C2×D411yescharacteristic
94C2×Q8×C11—24no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107Q8×D11—432no—
108C2×C4×D11—28no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—22no—
116C2×C4×D11—44no—
117C2×C4×D11—44no—
118C2×C4×D11SD1614yes—
119C2×C4×D11Q1614yes—
120C2×C4×D11#4114yes—
121C2×Dic22—28no—
122C2×Dic22—24no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—24no—
126C2×Dic22—24no—
127C2×Dic22—44no—
128C2×Dic22—44no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4C2×D414yes—
140C42×C11C2×D412yes—
141C42×C11C2×D412yes—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11—44no—
146C4⋊Dic11—42no—
147C4⋊Dic11—42no—
148C4⋊Dic11C2×D414yes—
149Dic11⋊C4—28no—
150Dic11⋊C4—28no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C4×Dic11—21no—
154C4×Dic11—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C22×C4⋊Q8—111no—
159C2×#487—111no—
160C2×#487—111no—
161#2857—111no—
162#2024—114no—
163#1990—111no—
164#1990D1111yescharacteristic, complemented
165#1872—114no—
166C4×C22⋊C8—111no—
167C23×C11C22×D411yescharacteristic
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11#12412yes—
173C22×D11C2×SD1612yes—
174C22×D11C2×Q1612yes—
175Q8×C11—48no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11#12012yes—
183C2×C4×C11#12012yes—
184C2×C4×C11C2×SD1612yes—
185C2×C4×C11C2×Q1612yes—
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11#13712yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4112yes—
191C2×C4×C112−1+412yes—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—24no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11#12412yes—
205C2×Dic11C2×SD1612yes—
206C2×Dic11C2×Q1612yes—
207C4×D11—24no—
208C4×D11—24no—
209C4×D11—28no—
210C4×D11—28no—
211C4×D11—416no—
212Dic22—416no—
213Dic22—48no—
214Dic22—44no—
215Dic22—44no—
216C8×C11—42no—
217C11⋊C8—42no—
218C23×Q8—221no—
219C2×C4⋊Q8—112no—
220C2×C4⋊Q8—111no—
221C2×C4⋊Q8—111no—
222C2×C4⋊Q8—221no—
223C2×C4⋊Q8—221no—
224C2×C4⋊Q8—224no—
225C2×C4⋊Q8—224no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C22⋊Q8—112no—
228C22×C4⋊C4—112no—
229C22×C4⋊C4—221no—
230C22×C42—111no—
231#487—224no—
232#487—224no—
233C2×#103—114no—
234C2×#103—114no—
235C2×C22⋊C8—112no—
236C2×C4×C8—111no—
237C2×C4×C8C2×D1111yescharacteristic
238#391—112no—
239#389—221no—
240#389—221no—
241#384C2×D1111yescharacteristic
242#380—221no—
243#380—221no—
244#340—114no—
245#340C2×D1114yes—
246#336—112no—
247C22×C11C2×#12011yescharacteristic
248C22×C11C2×#12411yescharacteristic
249C22×C11#53611yescharacteristic
250C22×C11C22×SD1611yescharacteristic
251C22×C11C22×Q1611yescharacteristic
252C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—22no—
260C2×D11#48714yescomplemented
261C4×C11—44no—
262C4×C11—82no—
263C4×C11#45014yes—
264C4×C11#45114yes—
265C4×C11#54812yes—
266C4×C11#54812yes—
267Dic11—22no—
268Dic11—22no—
269Dic11—22no—
270Dic11—44no—
271Dic11—82no—
272C22×Q8—21no—
273C22×Q8—112no—
274C22×Q8—222no—
275C22×Q8—228no—
276C22×Q8—221no—
277C22×Q8—444no—
278C22×Q8—444no—
279C23×C4—111no—
280C23×C4—111no—
281C23×C4—111no—
282C23×C4—222no—
283C22×C8—112no—
284C22×C8C22×D1112yes—
285C4⋊Q8—22no—
286C4⋊Q8—114no—
287C4⋊Q8—224no—
288C4⋊Q8—228no—
289C4⋊Q8—228no—
290C4⋊Q8—224no—
291C4⋊Q8—222no—
292C4⋊Q8—222no—
293C4⋊Q8—222no—
294C4⋊Q8D4414yes—
295C22⋊Q8—228no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—224no—
301C2×C4⋊C4—228no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22×D1112yes—
310C2×C4⋊C4C22×D1112yes—
311C2×C22⋊C4—222no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—222no—
316C2×C42—222no—
317C2×C42C22×D1111yescharacteristic
318#103—228no—
319#103—228no—
320C22⋊C8—224no—
321C4×C8—22no—
322C4×C8—222no—
323#95—222no—
324#95—222no—
325C2×C11#243611yescharacteristic
326C2×C11C2×#45011yescharacteristic
327C2×C11C2×#45111yescharacteristic
328C2×C11C2×#48711yescharacteristic
329C2×C11#314111yescharacteristic
330C2×C11#322911yescharacteristic
331C2×C11#323011yescharacteristic
332D11—24no—
333C24—111no—
334C2×Q8—24no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—228no—
338C2×Q8—224no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—224no—
342C2×Q8—224no—
343C2×Q8—444no—
344C2×Q8—444no—
345C2×Q8—4432no—
346C2×Q8—442no—
347C2×Q8—442no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—114no—
354C22×C4—114no—
355C22×C4—114no—
356C22×C4—228no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—444no—
367C22×C4—444no—
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—114no—
383C4⋊C4—228no—
384C4⋊C4—228no—
385C4⋊C4—224no—
386C4⋊C4—222no—
387C4⋊C4—444no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4C2×D4414yes—
391C22⋊C4—444no—
392C42—222no—
393C42—222no—
394C42—221no—
395C42—221no—
396C42C2×D4412yes—
397C42D4×D1112yes—
398C11#2590211yescharacteristic, complemented, Sylow
399C23—112no—
400C23—112no—
401C23—112no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—221no—
406C23C2×D4×D1111yescharacteristic
407Q8—48no—
408Q8—4416no—
409Q8—448no—
410Q8—444no—
411Q8—444no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—112no—
419C2×C4—112no—
420C2×C4—112no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—224no—
428C2×C4—228no—
429C2×C4—224no—
430C2×C4—228no—
431C2×C4—224no—
432C2×C4—4416no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4#6693512yes—
439C2×C4#6693512yes—
440C2×C4#6696412yes—
441C2×C4SD16×D1112yes—
442C2×C4#6696812yes—
443C2×C4Q16×D1112yes—
444C2×C4C22×D4411yescharacteristic
445C2×C4C2×D4×D1111yescharacteristic
446C2×C4#6704012yes—
447C2×C4#41×D1112yes—
448C8—42no—
449C8—442no—
450C22—114no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—222no—
456C22—222no—
457C22C2×#6693511yescharacteristic
458C22D11×#12411yescharacteristic
459C22#1062325511yescharacteristic
460C22C2×#6696411yescharacteristic
461C22C2×SD16×D1111yescharacteristic
462C22C2×#6696811yescharacteristic
463C22C2×Q16×D1111yescharacteristic
464C4—44no—
465C4—82no—
466C4—222no—
467C4—222no—
468C4—222no—
469C4—444no—
470C4—882no—
471C4#1062238914yes—
472C4#1062242114yes—
473C4#1062310712yes—
474C4#1062316412yes—
475C2—224no—
476C2#1307227311yescharacteristic
477C2C2×#1062238911yescharacteristic
478C2C2×#1062242111yescharacteristic
479C2D11×#48711yescharacteristic
480C2#1307900611yescharacteristic
481C2#1307976111yescharacteristic
482C2#1307976811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1990D11
hypocenterC11#25902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622706C2semidirect
3. C2×#10622294C2semidirect
5. #13069756C2semidirect
6. #13069576C2semidirect
9. C11×#1990C2semidirect
164. #1990D11semidirect
260. C2×D11#487semidirect
398. C11#25902semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D11×C4⋊Q82
C2×#106227062
C2×#106222942
#130769692
#130697562
#130695762
#130689222
C4×(C2×D11)⋊C82
C11×#19902
#2590211